Criminal convictions, Moral turpitude and admission to the US

I had several convictions during my early 20s, in my country of origin. However I did only ever serve one term of imprisonment of 2yrs (actually served 13 months as I got early release for good behaviour).

Since moving to Australia, I have only had traffic related offences, and a disorderly conduct, the last of which was back in 1995 or 1996. Since then I have not been charged with any offence. Fines and disqualification from driving were the sentences imposed for these transgressions.

I am in contact with a lady in the US who would like me to visit her with a view to marriage. I can enter the US under the visa waiver program on my Australian passport. My concern is if I would be questioned about my country of origin as the city of my birth is listed on the passport. Or would immigration simply check my Australian records?

The problem is that though my last conviction in my country of origin was now 15 years ago, I have some convictions recorded in that country that might be considered crimes of moral turpitude, eg burglary, and "being a party to an aggravated robbery" (in the wrong company at the time, and one of the persons went off and tried to hold up a 7/11 type store with an air pistol. I got 2 years probation as I was not actually a principle offender). These offences took place back in the early 80s.

There was also an incident (1991) where the person I was staying with was going to attack my then wife. He made a grab for a knife, I got to it first and waved it at him as he tried to assault me. He came off second best, so I ended up getting charged with, "assault using a knife as a weapon". This is the conviction I was imprisoned for.

Also I realise that if this lady and I were to marry, then somewhere down the track all this stuff is likely to come out, and that does concern me as who I was at at 20 or 30, I am not at 45. If I had such bad moral character I'm pretty sure the Australian government would not have granted me citizenship, but we are dealing with the United States government in this situation and their rules may be different.

To summarise:
1. Do you think I should first obtain a visa or just enter on the VWP, knowing that I have committed no crimes of moral turpitude or been imprisoned in the 13 years I have lived in Australia?

2.Will my past comeback to haunt me if I marry this woman and she files an I-130 ? Would I after marrying her then be in danger of being deported? Would I still be able to naturalize later?

3. If we married in the US could I adjust a tourist visa or my status on the visa waiver program from within the US? Or would I have to leave the US first and seek reentry under the K3 class visa?

Many thanks for your advice. It's very much appreciated.